IRREDUCIBLE CONVEX PAVING FOR DECOMPOSITION OF MULTIDIMENSIONAL MARTINGALE TRANSPORT PLANS

• 成果类型: Article
• 署名作者: De March, Hadrien; Touzi, Nizar
• 署名单位: Institut Polytechnique de Paris; Ecole Polytechnique
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/18-AOP1295
• 发表日期: 2019
• 页码: 1726-1774
• 关键词: Bounds

摘要

Martingale transport plans on the line are known from Beiglbock and Juillet (Ann. Probab. 44 (2016) 42-106) to have an irreducible decomposition on a (at most) countable union of intervals. We provide an extension of this decomposition for martingale transport plans in R-d, d >= 1. Our decomposition is a partition of R-d consisting of a possibly uncountable family of relatively open convex components, with the required measurability so that the disintegration is well defined. We justify the relevance of our decomposition by proving the existence of a martingale transport plan filling these components. We also deduce from this decomposition a characterization of the structure of polar sets with respect to all martingale transport plans.